Transmeningeal delivery refers to a treatment modality in which drugs and other therapeutic agents are delivered into a cranial subarachnoid space to allow them to diffuse through the pia mater into an underlying, diseased cerebral cortical area and thereby correct abnormal neural functions in that cortical area. Neurological disorders with focal cerebral cortical pathology include various forms of focal epilepsy, stroke, traumatic brain injury, and tumors. Although drug delivery directly into the subdural/subarachnoid space of the spinal cord (“intrathecal administration”) is widely used in clinical practice for pain relief in obstetric anesthesia, as well as in lower abdominal, urogenital, rectal and lower extremity surgical procedures, the subdural/subarachnoid compartment of the brain is currently not utilized for therapeutic purposes, such as for the treatment of cerebral cortical disorders. This is due to a lack of appropriate devices which are both implantable in the subdural/subarachnoid space without causing significant damage to neural tissue and can also perform localized medication delivery for long periods without an eventual clogging or obstruction in their delivery systems rendering them incapable of functioning as intended. Current experimental or clinically used cannulas, catheters or drug-releasing polymers share the same common problem that bedevils their use. This problem is the induction of inflammatory host responses that encapsulate or clog the implant, preventing its ability to maintain constant, or at least sufficient, therapeutic agent delivery with consequent therapeutic effects. The inflammatory host response is mediated by cells, such as mast cells, macrophages, lymphocytes, fibroblasts and other cellular elements, and by molecules, such as various collagen, elastin, proteoglycans, adhesive glycoproteins and other molecules, which, together accumulate and aggregate, forming a fibrous, gelatinous layer over the dorsal surface of the cerebral cortex and its covering pia mater within 2-3 weeks. This layer of newly generated connective tissue forms a lasting barrier to drugs or other medications and therapeutic agents delivered into the subarachnoid space, effectively blocking their transmeningeal influx into the cortical tissue. As a consequence, presently used or experimental needles, cannulas, catheters, or drug-releasing polymers cannot provide treatment for cerebral cortical disorders for periods longer than 2-3 weeks. This forbids their implantation for the treatment of chronic cerebral cortical disorders, the treatment of which requires persistent treatment over a period of several month or years.